{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sebastian Raschka 2014"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load_ext watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "last updated: 2016-07-11 \n",
      "\n",
      "CPython 3.5.1\n",
      "IPython 4.2.0\n",
      "\n",
      "scipy 0.17.1\n",
      "scikit-learn 0.17.1\n",
      "numpy 1.11.0\n",
      "matplotlib 1.5.1\n"
     ]
    }
   ],
   "source": [
    "%watermark -v -u -d -p scipy,scikit-learn,numpy,matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font size=\"1.5em\">[More information](https://github.com/rasbt/watermark) about the `watermark` magic command extension.</font>\n",
    "\n",
    "\n",
    "<hr>\n",
    "I would be happy to hear your comments and suggestions. \n",
    "Please feel free to drop me a note via\n",
    "[twitter](https://twitter.com/rasbt), [email](mailto:bluewoodtree@gmail.com), or [google+](https://plus.google.com/+SebastianRaschka).\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kernel tricks and nonlinear dimensionality reduction via PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Principal Component Analysis](#Principal-Component-Analysis)\n",
    "- [PCA and linear dimensionality reduction](#PCA-and-linear-dimensionality-reduction)\n",
    "- [Nonlinear dimensionality reduction](#Nonlinear-dimensionality-reduction)\n",
    "- [Kernel functions and the kernel trick](Kernel-functions-and-the-kernel-trick)\n",
    "- [Gaussian RBF Kernel PCA](#Gaussian-RBF-Kernel-PCA)\n",
    "- [Implementing the RBF kernel PCA step-by-step](#Implementing-the-RBF-kernel-PCA-step-by-step)\n",
    "- [Examples of RBF Kernel PCA](#Examples-of-RBF-Kernel-PCA)\n",
    "    - [Half-moon shapes](#Half-moon-shapes)\n",
    "    - [Concentric circles](#Concentric-circles)\n",
    "    - [Swiss roll](#Swiss-roll)\n",
    "- [Appendix A: Projecting new data](#Appendix-A:-Projecting-new-data)\n",
    "- [References](#References)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Most machine learning algorithms have been developed and statistically validated for linearly separable data. Popular examples are linear classifiers like Support Vector Machines (SVMs) or the (standard) Principal Component Analysis (PCA) for dimensionality reduction. However, most real world data requires nonlinear methods in order to perform tasks that involve the analysis and discovery of patterns successfully.**\n",
    "\n",
    "**The focus of this article is to briefly introduce the idea of kernel methods and to implement a Gaussian radius basis function (RBF) kernel that is used to perform nonlinear dimensionality reduction via BF kernel principal component analysis (kPCA).**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principal Component Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main purpose of principal component analysis (PCA) is the analysis of data to identify patterns that represent the data \"well.\" The principal components can be understood as new axes of the dataset that maximize the variance along those axes (the eigenvectors of the covariance matrix). In other words, PCA aims to find the axes with maximum variances along which the data is most spread.\n",
    "\n",
    "![pca overview](../../Images/kernel_pca/pca_1.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA and linear dimensionality reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A common application of PCA is to reduce the dimensions of the dataset with minimal loss of information.\n",
    "Here, the entire dataset (*d* dimensions) is projected onto a new subspace (*k* dimensions where *k* < *d*). \n",
    "This method of projection is useful in order to reduce the computational costs and the error of parameter estimation (\"curse of dimensionality\").\n",
    "\n",
    "The standard PCA approach can be summarized in six simple steps:\n",
    "\n",
    "![pca overview](../../Images/kernel_pca/pca_2.png)\n",
    "\n",
    "More details can be found in a previous article [\"Implementing a Principal Component Analysis (PCA) in Python step by step\"](http://sebastianraschka.com/Articles/2014_pca_step_by_step.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonlinear dimensionality reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The \"classic\" PCA approach described above is a linear projection technique that works well if the data is linearly separable. However, in the case of linearly inseparable data, a nonlinear technique is required if the task is to reduce the dimensionality of a dataset.\n",
    "\n",
    "![linear and nonlinear data](../../Images/kernel_pca/linear_vs_nonlinear.png)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kernel functions and the kernel trick"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The basic idea to deal with linearly inseparable data is to project it onto a higher dimensional space where it becomes linearly separable. Let us call this nonlinear mapping function $\\phi$ so that the mapping of a sample $\\mathbf{x}$ can be written as $\\mathbf{x} \\rightarrow \\phi (\\mathbf{x})$, which is called \"kernel function.\" \n",
    "\n",
    "Now, the term \"kernel\" describes a function that calculates the dot product of the images of the samples $\\mathbf{x}$ under $\\phi$.\n",
    "\n",
    "\n",
    "\\begin{equation}\\kappa(\\mathbf{x_i, x_j}) =  \\phi (\\mathbf{x_i}) \\phi (\\mathbf{x_j})^T    \\end{equation}\n",
    "\n",
    "More details about the derivation of this equation are provided in this excellent review article by Quan Wang: [Kernel Principal Component Analysis and its Applications in Face Recognition and Active Shape Models](http://arxiv.org/abs/1207.3538).[[1](#References)]\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In other words, the function $\\phi$ maps the original d-dimensional features into a larger, k-dimensional feature space by creating nononlinear combinations of the original features. For example, if $\\mathbf{x}$ consists of 2 features:\n",
    "\n",
    "\\begin{equation} \\mathbf{x} = \\big[x_1 \\quad x_2\\big]^T \\quad \\quad \\mathbf{x} \\in I\\!R^d\\\\\n",
    "\\Downarrow \\phi \\\\\n",
    " \\mathbf{x}' = \\big[x_1 \\quad x_2 \\quad x_1 x_2 \\quad x_{1}^2 \\quad x_1 x_{2}^3 \\quad \\dots \\big]^T \\quad \\quad \\mathbf{x} \\in I\\!R^k (k >> d) \\end{equation}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often, the mathematical definition of the RBF kernel is written and implemented as\n",
    "\n",
    "\\begin{equation} \\kappa(\\mathbf{x_i, x_j}) = exp\\bigg(- \\gamma \\; \\lVert\\mathbf{x_i - x_j }\\rVert^{2}_{2} \\bigg)\\end{equation}\n",
    "\n",
    "where $\\textstyle\\gamma = \\tfrac{1}{2\\sigma^2}$ is a free parameter that is to be optimized. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian radial basis function (RBF) Kernel PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the linear PCA approach, we are interested in the principal components that maximize the variance in the dataset. This is done by extracting the eigenvectors (principle components) that correspond to the largest eigenvalues based on the covariance matrix:\n",
    "\n",
    "\\begin{equation}\\text{Cov} = \\frac{1}{N} \\sum_{i=1}^{N} \\mathbf{x_i} \\mathbf{x_i}^T \\end{equation}\n",
    "\n",
    "Bernhard Scholkopf ([Kernel Principal Component Analysis](http://dl.acm.org/citation.cfm?id=299113) [[2](#References)]) generalized this approach for data that was mapped onto the higher dimensional space via a kernel function:\n",
    "\n",
    "\\begin{equation}\\text{Cov} = \\frac{1}{N} \\sum_{i=1}^{N} \\phi(\\mathbf{x_i}) \\phi(\\mathbf{x_i})^T \\end{equation}\n",
    "\n",
    "However, in practice the the covariance matrix in the higher dimensional space is not calculated explicitly (kernel trick). Therefore, the implementation of RBF kernel PCA does not yield the principal component axes (in contrast to the standard PCA), but the obtained eigenvectors can be understood as projections of the data onto the principal components."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing the RBF kernel PCA step-by-step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to implement the RBF kernel PCA we just need to consider the following two steps.\n",
    "\n",
    "##### 1. Computation of the kernel (similarity) matrix.\n",
    "\n",
    "In this first step, we need to calculate \n",
    "\n",
    "\\begin{equation} \\kappa(\\mathbf{x_i, x_j}) = exp\\bigg(- \\gamma \\; \\lVert\\mathbf{x_i - x_j }\\rVert^{2}_{2} \\bigg)\\end{equation}\n",
    "\n",
    "for every pair of points. E.g., if we have a dataset of 100 samples, this step would result in a symmetric 100x100 kernel matrix.\n",
    "\n",
    "##### 2. Eigendecomposition of the kernel matrix.\n",
    "\n",
    "Since it is not guaranteed that the kernel matrix is centered, we can apply the following equation to do so:\n",
    "\n",
    "\\begin{equation} K' = K - \\mathbf{1_N} K - K \\mathbf{1_N} + \\mathbf{1_N} K \\mathbf{1_N} \\end{equation}\n",
    "\n",
    "where $\\mathbf{1_N}$ is (like the kernel matrix) a $N\\times N$ matrix with all values equal to $\\frac{1}{N}$. [[3](#References)]\n",
    "\n",
    "Now, we have to obtain the eigenvectors of the centered kernel matrix that correspond to the largest eigenvalues. Those eigenvectors are the data points already projected onto the respective principal components. \n",
    "\n",
    "\n",
    "Below, we implement those steps in Python to see how those computations work."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.spatial.distance import pdist, squareform\n",
    "from scipy import exp\n",
    "from scipy.linalg import eigh\n",
    "import numpy as np\n",
    "\n",
    "def stepwise_kpca(X, gamma, n_components):\n",
    "    \"\"\"\n",
    "    Implementation of a RBF kernel PCA.\n",
    "    \n",
    "    Arguments:\n",
    "        X: A MxN dataset as NumPy array where the samples are stored as rows (M),\n",
    "           and the attributes defined as columns (N).\n",
    "        gamma: A free parameter (coefficient) for the RBF kernel.\n",
    "        n_components: The number of components to be returned.\n",
    "    \n",
    "    \"\"\"\n",
    "    # Calculating the squared Euclidean distances for every pair of points\n",
    "    # in the MxN dimensional dataset.\n",
    "    sq_dists = pdist(X, 'sqeuclidean')\n",
    "\n",
    "    # Converting the pairwise distances into a symmetric MxM matrix.\n",
    "    mat_sq_dists = squareform(sq_dists)\n",
    "\n",
    "    # Computing the MxM kernel matrix.\n",
    "    K = exp(-gamma * mat_sq_dists)\n",
    "\n",
    "    # Centering the symmetric NxN kernel matrix.\n",
    "    N = K.shape[0]\n",
    "    one_n = np.ones((N,N)) / N\n",
    "    K = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n)\n",
    "\n",
    "    # Obtaining eigenvalues in descending order with corresponding \n",
    "    # eigenvectors from the symmetric matrix.\n",
    "    eigvals, eigvecs = eigh(K)\n",
    "\n",
    "    # Obtaining the i eigenvectors that corresponds to the i highest eigenvalues.\n",
    "    X_pc = np.column_stack((eigvecs[:,-i] for i in range(1,n_components+1)))\n",
    "    \n",
    "    return X_pc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples of RBF Kernel PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, we will apply the RBF kernel PCA to different nonlinear sample data in order to perform dimensionality reduction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Half-moon shapes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will start with a simple example of 2 half-moon shapes generated by the [`make_moons`](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_moons.html) function from [scikit-learn](http://scikit-learn.org/stable/index.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BAICuWPKVLuo+DawCANBXr5ngzBBvD+q4uVgGmCMAACaDGeLtQV02G18HDGBi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\nBAAAACSIAAAAgAT9fytWsXwo8ppeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b47f5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.datasets import make_moons\n",
    "X, y = make_moons(n_samples=100, random_state=123)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "\n",
    "plt.scatter(X[y==0, 0], X[y==0, 1], color='red', alpha=0.5)\n",
    "plt.scatter(X[y==1, 0], X[y==1, 1], color='blue', alpha=0.5)\n",
    "\n",
    "plt.title('A nonlinear 2Ddataset')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.xlabel('x coordinate')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the two half-moon shapes are linearly inseparable, we expect that the \"classic\" PCA will fail to give us a \"good\" representation of the data in 1D space. Here, we will use the [`PCA`](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) class that is implemented in scikit-learn to perform the dimensionality reduction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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glnN+8ylyLnNpcv0aKO3aVTyuqbINgDQNpiyl6bCB0tyYAZAm5ZBxrWMyp0KO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\nkjrIAECSpA4yAJAkqYMMACRJ6qD/DzKmUIL/usy8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e6d9a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "scikit_pca = PCA(n_components=2)\n",
    "X_spca = scikit_pca.fit_transform(X)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_spca[y==0, 0], X_spca[y==0, 1], color='red', alpha=0.5)\n",
    "plt.scatter(X_spca[y==1, 0], X_spca[y==1, 1], color='blue', alpha=0.5)\n",
    "\n",
    "plt.title('First 2 principal components after Linear PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f7642b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "scikit_pca = PCA(n_components=1)\n",
    "X_spca = scikit_pca.fit_transform(X)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_spca[y==0, 0], np.zeros((50,1)), color='red', alpha=0.5)\n",
    "plt.scatter(X_spca[y==1, 0], np.zeros((50,1)), color='blue', alpha=0.5)\n",
    "\n",
    "plt.title('First principal component after Linear PCA')\n",
    "plt.xlabel('PC1')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the resulting principal components do not yield a subspace where the data is linearly separated well. Note that PCA is a unsupervised method and does not \"consider\" class labels in order to maximize the variance in contrast to [Linear Discriminant Analysis](http://sebastianraschka.com/Articles/2014_python_lda.html). Here, the colors blue and red are just added for visualization purposes to indicate the degree of separation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian RBF kernel PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will perform dimensionality reduction via RBF kernel PCA on our half-moon data. The choice of $\\gamma$ depends on the dataset and can be obtained via hyperparameter tuning techniques like Grid Search. Hyperparameter tuning is a broad topic itself, and here I will just use a $\\gamma$-value that I found to produce \"good\" results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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2P7Djxo3T5z//eb3xjW/U5MmTdcEFF+iJJ57QUUcdpSlTpuiUU07RK6+8UnPdK1eu7Hj+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f7b9a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_pc = stepwise_kpca(X, gamma=15, n_components=2)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_pc[y==0, 0], X_pc[y==0, 1], color='red', alpha=0.5)\n",
    "plt.scatter(X_pc[y==1, 0], X_pc[y==1, 1], color='blue', alpha=0.5)\n",
    "\n",
    "plt.title('First 2 principal components after RBF Kernel PCA')\n",
    "plt.text(-0.18, 0.18, 'gamma = 15', fontsize=12)\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VPBU98URxPaJ4uti0qfHeU5R9/vPhpz91RqBmJM0EDMVQOt7ylX7hwoVbLvf0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f7bfba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_pc[y==0, 0], np.zeros((50)), color='red', alpha=0.5)\n",
    "plt.scatter(X_pc[y==1, 0], np.zeros((50)), color='blue', alpha=0.5)\n",
    "\n",
    "plt.title('First principal component after RBF Kernel PCA')\n",
    "plt.text(-0.17, 0.007, 'gamma = 15', fontsize=12)\n",
    "plt.xlabel('PC1')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can clearly see that the projection via RBF kernel PCA yielded a subspace where the classes are separated well. Such a subspace can then be used as input for linear classification models, such as Support Vector Machines or naive Bayes classifiers, which will be covered in future articles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### scikit RBF kernel PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For our convenience, there is already an implementation of the [`KernelPCA`](http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.KernelPCA.html) in scikit-learn. \n",
    "Let us confirm that the results of our implementation is consistent with scikit-learn's approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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18GZVU5JeSCX5Gma5cII3K6OS9EIqydcwy4UTvFkZlaQXUkm+hlkufA7erMxK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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f2f438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import KernelPCA\n",
    "\n",
    "scikit_kpca = KernelPCA(n_components=2, kernel='rbf', gamma=15)\n",
    "X_skernpca = scikit_kpca.fit_transform(X)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_skernpca[y==0, 0], X_skernpca[y==0, 1], color='red', alpha=0.5)\n",
    "plt.scatter(X_skernpca[y==1, 0], X_skernpca[y==1, 1], color='blue', alpha=0.5)\n",
    "\n",
    "plt.text(-0.48, 0.35, 'gamma = 15', fontsize=12)\n",
    "plt.title('First 2 principal components after RBF Kernel PCA via scikit-learn')\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7NtROY5k+66bJoTLtHsJobdJeyvRjl+tl+bY+3YaWbe1TvnH+r3+9+aXpiSc2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\nhTDUJUkqhKEuSVIhDHVJkgrx/wEDDT5hPIQuyAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f9b780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scikit_kpca = KernelPCA(n_components=1, kernel='rbf', gamma=15)\n",
    "X_skernpca = scikit_kpca.fit_transform(X)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_skernpca[y==0, 0], np.zeros((50,1)), color='red', alpha=0.5)\n",
    "plt.scatter(X_skernpca[y==1, 0], np.zeros((50,1)), color='blue', alpha=0.5)\n",
    "plt.text(-0.48, 0.007, 'gamma = 15', fontsize=12)\n",
    "plt.title('First principal component after RBF Kernel PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Concentric circles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For our next example, we will have a look at the classic case of 2 concentric circles with random noise produced by scikit-learn's [`make_circles`](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_circles.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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z7hiisjJaDN75ThuHkGybRpqbbYQhLgBhMMNpJo51bKOY3HknrQHTpwP/8A/A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\nqB/6kAo+frfQ+73d5+zbp3Lr66/ra35DdccOTQff1aU7/dNPVzNDX5/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pfUaffBL4wz8s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Pj4BIBvA4AxZiuAY0SkHckj7LOUeKflbEh3T45TOKYQ6joBBYynJExiTCQUjg4Ana7/d2ePJYnp\nxphuADDGvAVgesB5SRxTYcaH95w9PuckgbDP0uKsWvthETmjPF2rOTimwhN5PFVLGKAvTCQUnpiu\n1YQnx3Xys5kFecgmYkyRkvI0gBOMMQNZNfePAZxW4T6R2qWg8VTVAoAxZlkMbezN/t4vIg9A1XMT\nbrKO4VrtAXCC6//js8cmFLmuU9bJpt0Y0y0iMwDsC2gjEWPKQ5jxsQfA7DznJIG818oY0+/6+xER\nuV1E2owxB8vUx1qBYyoEhY6niWICCEwkJCLN2b9tIqHnytmxKiTITvQUgFNE5EQRSQH4CwAPlq9b\nVcGDAFZm//4cgP/0npDgMRVmfDwI4LMAICIfANBrTSoJI++1ctuxRWQRNCQ7qYu/IHhe4phyCLxO\nhY6nqtYA5EJEPgngFgDHQhMJPWuM+aiIzATwLWPMRVBV7wPZFMGTAHwviYmEwlwrY8yIiFwC4FGo\nYHinMebFCna7ElwP4PsishrAGwA+A2hyKiR8TAWNDxH5vL5svmmM+S8R+ZiI/A5ABsCqSva5UoS5\nVgAuFpG/AXAEwCCAP69cjyuHiPw7gCUAponImwCuAZACx9QY8l0nFDiemAiIEEIISSATxQRACCGE\nkAhQACCEEEISCAUAQgghJIFQACCEEEISCAUAQgghJIFQACCEEEISCAUAQkjsiMhrItKW/bvgLIki\n8rlsVkZCSMxQACCEFIWI1PscfjfBiDHmg0U0vxIs/kJISaAAQMgEQUTOEZHfikhKRNIi8pxfVTAR\n+Wz2vGdE5J7ssRNF5LFsNbGNInJ8nuMbRORfReRJANeLSJuI/FREdojIt+BKWSoi72R/ny8ij4vI\nD0TkRRH5juucq0Rkq4hsF5E7ssf+FMA5AL4rIr8RkckicraIbMpWYnwkiaVhCYkLZgIkZAIhIusA\nTMn+dBpjrve8fgaAHwFYbIzpEZEWY0yviDwI4PvGmO+KyCoAf2KM+VSO4xsATDPG/Em23ZsA7DfG\nfFVEPgbgIQDHGWMOikifMWaqiJwPrVJ2BoC3AGwGcLkxZovtR7atbwP4D2PMwyLyOID/Z4x5RkQm\nAfh5tg8HROQzAD5ijPnLkl5UQiYoNVsLgBDiy3poMZpBAJf6vP5hAD8wxvQAgF10ASwG8Kns39+B\n1kXIdRwAfuD6+w/tedn87T0B/dtmqymKyLMATgKwBcAficgVAJoAtEILLD2cfY/VJswDcCa0BLNA\nNZhdAZ9DCMkDBQBCJhbHAmiGPtuNUEEgDIWoAjM53h9U3e2w6+8RAJNEZDKA2wCcbYzpEpFroH33\nIgCeM8acV0BfCSEe6ANAyMTiDgBfAvA9AF/zef1nAP7M5aHfmj2+BcCK7N//G8Avs39vDjju5RcA\n/le2zY8CaHG9FiQMWBqhAsSBbKnli12vvQNgavbvnQCOy5aFhYhM8vNxIISEgxoAQiYIIvJ/AAwb\nY+4TkToAm0VkiTFmkz3HGPOCiPwTgJ+LyFEAzwBYDeCLADaIyOUA9sMpuxp03LvjXwfgXhH5C6gw\n8abrtSDtgsn26ZCI/BuA5wHsBbDNdc7dAO4QkQGoOeLPANwsIscAqAdwI4AX8l4cQsg46ARICCGE\nJBCaAAghhJAEQgGAEEIISSAUAAghhJAEQgGAEEIISSAUAAghhJAEQgGAEEIISSAUAAghhJAEQgGA\nEEIISSD/H/z4uQFlXJmBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11131feb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_circles\n",
    "\n",
    "X, y = make_circles(n_samples=1000, random_state=123, noise=0.1, factor=0.2)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "\n",
    "plt.scatter(X[y==0, 0], X[y==0, 1], color='red', alpha=0.5)\n",
    "plt.scatter(X[y==1, 0], X[y==1, 1], color='blue', alpha=0.5)\n",
    "plt.title('Concentric circles')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.xlabel('x coordinate')\n",
    "plt.savefig('/Users/Sebastian/Desktop/circles1.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qnj8/b921t/dseba09JzTG0wZtcNt7e35b1dXnjZ9eh5c0PMhqe1BjaXaXvZE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\nJKkQ/xcgYwtW5IaDKwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111463828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scikit_pca = PCA(n_components=2)\n",
    "X_spca = scikit_pca.fit_transform(X)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X[y==0, 0], np.zeros((500,1))+0.1, color='red', alpha=0.5)\n",
    "plt.scatter(X[y==1, 0], np.zeros((500,1))-0.1, color='blue', alpha=0.5)\n",
    "plt.ylim([-15,15])\n",
    "plt.text(-0.125, 12.5, 'gamma = 15', fontsize=12)\n",
    "plt.title('First principal component after Linear PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.savefig('/Users/Sebastian/Desktop/circles2.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the results obtained via the linear PCA approach does not produce a subspace where the 2 classes are linearly well separated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian RBF kernel PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4lxICuq0bEaszc2JDG6syc1I32zcEbE933VUeadvzNt5tt/JKsMceJfp3dg6q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\nbfP4M/PBzLyzWr4WuJst30u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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b47f320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_pc = stepwise_kpca(X, gamma=15, n_components=1)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_pc[y==0, 0], np.zeros((500,1)), color='red', alpha=0.5)\n",
    "plt.scatter(X_pc[y==1, 0], np.zeros((500,1)), color='blue', alpha=0.5)\n",
    "plt.text(-0.05, 0.007, 'gamma = 15', fontsize=12)\n",
    "plt.title('First principal component after RBF Kernel PCA')\n",
    "plt.xlabel('PC1')\n",
    "\n",
    "plt.savefig('/Users/Sebastian/Desktop/circles3.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And again, this 1-dimensional subspace obtained via Gaussian RBF kernel PCA looks much better in terms of linear class separation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Swiss roll"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unrolling the famous Swiss roll is a more challenging task than the examples we have seen above. We will use the [`make_swiss_roll`](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_swiss_roll.html) to create 3-dimensional Swiss roll and start with the linear PCA to project the dataset onto a 2D and 1D feature subspace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ISkpi1YoV9Mg7zDU57bigTSsuUMl8M+t9vF5vk7r/DWl3FJyUr2sV5SuvvEK/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pAAAg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J6NXg5uaGTqcjKyurWMH3gsjKyhKrYouLudoWYQIUmiEZW9BXVCZXYVizgEwQF6Gy2NzRh0Kh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\nUIiISBQMFCIiEgUDhYiIRPEP7ITXiLTY0YAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083a7fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_swiss_roll\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "X, color = make_swiss_roll(n_samples=800, random_state=123)\n",
    "\n",
    "fig = plt.figure(figsize=(7,7))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.scatter(X[:, 0], X[:, 1], X[:, 2], c=color, cmap=plt.cm.rainbow)\n",
    "plt.title('Swiss Roll in 3D')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZSZJUonLlyhGdmk2VZWfw8b/CsfAkLtxPY8nJSE5HJtNvZxhtP2xVLLH+tmsX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KYL6/8kxplZ6sK6jhESExPL9RERRowcignBI3H24i506NQWO3ZsBwA4ODri4pmyYlqlJQrcvPwa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083a73c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "scikit_pca = PCA(n_components=2)\n",
    "X_spca = scikit_pca.fit_transform(X)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_spca[:, 0], X_spca[:, 1], c=color, cmap=plt.cm.rainbow)\n",
    "\n",
    "plt.title('First 2 principal components after Linear PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vvPMoKSlh06ZN/O1vfyMYDDJlyhSioqLYtGkTeXl5tLe3U11dTXFxMRERERiG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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10923e048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scikit_pca = PCA(n_components=1)\n",
    "X_spca = scikit_pca.fit_transform(X)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_spca, np.zeros((800,1)), c=color, cmap=plt.cm.rainbow)\n",
    "plt.title('First principal component after Linear PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian RBF kernel PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I haven't found a good $\\gamma$ parameter for the Gaussian RBF kernel for good linear separation of this dataset. The best result I obtained is shown in the following figures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lBw4cyOsQhRBC5DBJDoRZaGgoHTp0w8rSmoQre/gv7A+stHqql1uHyZRBfPJe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w/Cv0M7iles4p4+ffjqq68IbRIPgMlsxvf2DhQsX8bhnt2w1oykbOcOFs2fX8HvlIhcLs37iVQR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\nnqYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10834b668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_pc = stepwise_kpca(X, gamma=0.1, n_components=2)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_pc[:, 0], X_pc[:, 1], c=color, cmap=plt.cm.rainbow)\n",
    "\n",
    "plt.title('First 2 principal components after RBF Kernel PCA')\n",
    "plt.text(-0.14, 0.14, 'gamma = 0.1', fontsize=12)\n",
    "plt.xlabel('PC1')\n",
    "plt.ylabel('PC2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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du2Pv3r0IDAy8qIaFCxd6/p+SkoKUlJS2rBJjjDH2XyM9PR3p6enXdJkCteF0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\nWITgBwDAIgQ/AAAWIfgBALAIwQ8AgEUIfgAALEL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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083206d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_pc[:,0], np.zeros((800,1)), c=color, cmap=plt.cm.rainbow)\n",
    "\n",
    "plt.text(-0.125, 0.007, 'gamma = 0.1', fontsize=12)\n",
    "plt.title('First principal component after RBF Kernel PCA')\n",
    "plt.xlabel('PC1')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Locally-Linear Embedding (LLE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In 2000, Sam T. Roweis and Lawrence K. Saul ([Nonlinear dimensionality reduction by locally linear embedding](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.3313) [[4](#References)]) introduced an unsupervised learning algorithm called locally linear embedding (LLE) that is better suited to identify patterns in the high-dimensional feature space and solves our problem of nonlinear dimensionality reduction for the Swiss roll.   \n",
    "Here, we will use the [`locally_linear_embedding`](http://scikit-learn.org/stable/modules/generated/sklearn.manifold.locally_linear_embedding.html) class from scikit-learn to \"unroll\" the Swiss roll."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aS1IzHvLxx0HM+2GOHHr8X0qeopckSZLyCA0NZeHCRWRn59CnT0/q1asHQKUK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\nEEIIUQdJgRdCCCHqoP8DuNPe5hxyQmAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108f9f400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.manifold import locally_linear_embedding\n",
    "\n",
    "X_lle, err = locally_linear_embedding(X, n_neighbors=12, n_components=2)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_lle[:, 0], X_lle[:, 1], c=color, cmap=plt.cm.rainbow)\n",
    "\n",
    "plt.title('First 2 principal components after Locally Linear Embedding')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qqj9lCiGEEOKAfgV/dXU1mZmZwWGXy0V1dfUJzVNTU3PctgBPPfUU06ZN60+Z\nQgghhDigX8GvadoJzaeUOqn+H374Yex2O9dee+1JtRdCCCFEb9b+NM7IyKCysjI4XFlZicvl6nOe\nqqoqXC4Xfr+/z7bLli2juLiY999/v88a5s2bF/y7qKiIoqKik1wbIYQQ4pulpKSEkpKSU9up6ge/\n36/y8vLU3r17ldfrVSNHjlRlZWW95nnzzTfV1KlTlVJKrV69Wo0bN+64bd966y01ZMgQ1dDQ0Ofy\n+1m+EEIIcVo5FbnXrzN+q9XKwoULufjiizEMg1mzZjF48GAWL14MwK233sq0adMoLi4mPz8fp9PJ\n0qVL+2wLcNttt+Hz+ZgyZQoAEyZM4C9/+Ut/ShVCCCEEoB34BHFa0jTtpJ8fEEIIIU43pyL35Jf7\nhBBCiBAiwS+EEEKEEAl+IYQQIoRI8AshhBAhRIJfCCGECCES/EIIIUQIkeAXQgghQogEvxBCCBFC\nJPiFEEKIECLBL4QQQoQQCX4hhBAihEjwCyGEECFEgl8IIYQIIRL8QgghRAiR4BdCCCFCiAS/EEII\nEUIk+IUQQogQIsEvhBBChBAJfiGEECKESPALIYQQIUSCXwghhAghEvxCCCFECJHgF0IIIUKIBL8Q\nQggRQiT4hRBCiBAiwS+EEEKEEAl+IYQQIoRI8AshhBAhRIJfCCGECCES/EIIIUQIkeAXQgghQogE\nvxBCCBFCJPiFEEKIENLv4F+5ciWFhYUUFBSwYMGCo85z++23U1BQwMiRIyktLT1u2+bmZqZMmcLA\ngQO56KKLaG1t7W+ZQgghhAA0pZQ62caGYTBo0CDee+89MjIyOOuss1i+fDmDBw8OzlNcXMzChQsp\nLi5m7dq1/OQnP2HNmjV9tr3rrrtITEzkrrvuYsGCBbS0tDB//vwji9c0+lH+SWlpaeHjjz/mxRdf\nZP369ei6zoABA9i0aRMAcXFx1NfXY7fbKSoq4pprrmHDhg1s3LgRt9tNbW0tUVFRTJ8+ndjYWF59\n9VXa2tqIjo6mtLSUqKgoUlJS2LRpEy0tLYSFhTF69GgSExOJjo7m888/p6Ojg8LCQpqbmwFIT0+n\nsbGRiooKlFKMGDGCoUOH8t5776FpGk6nk71795KSkoLT6SQmJobMzExqamqYPHky9fX1vP7663g8\nHsLCwoiNjUUpxZ49e9B1nSFDhpCYmBisKT4+ns7OTjo7O3G5XOi6TmRkJGFhYXzxxRf4/X5iY2NJ\nTU0lMjItcLgNAAAgAElEQVQSgBEjRhAWFsbWrVtxuVwYhsGuXbvIyMigsrKSiooKmpqaaGlpwWaz\nkZmZSW5uLt3d3VgsFrKzs/F6vWRmZjJo0CAiIyPx+/0sX76cPXv2EB4ejtfrJSYmhsjISLq7u6ms\nrCQmJoacnBxWr15NZ2cnADExMeTm5tLR0UFcXBznnXceXV1d1NfXU1FRQUREBHFxcWzZsoW6ujpi\nY2MZOnQoW7ZswWq1kpGRQXl5Oc3NzYSFhZGSkkJDQwNKKWw2G06nk1GjRtHc3MzWrVsJBAIMGTKE\nUaNG8dRTT1FbW4vFYiEsLAyr1YphGGiaRmRkJJqmYbPZyM/PZ9euXfh8PmbNmsWsWbOYM2cOmzdv\npqCggOrqarZv305ERATf/va3yc7O5ssvv2T9+vXU1tYCEBUVxcCBAzFNk6qqKhISEhgwYACmaTJq\n1Cg+//xzKioqiI2NpaamhqamJhISEsjOzmbbtm243W7Cw8OJjo6ms7MTwzDw+/1YrVYyMzOJjo6m\nubmZ9vZ2vF4vDocDh8OBx+Nh9OjRXHzxxWzcuJEXXngBt9tNWloa3/rWt9i/fz9bt24FwOv1YrPZ\nSEhIYNKkSdTX17Ny5UqampoIDw8nJiaG/Px8nE4nO3bsCO4LAJs3b6aurg6Hw0FaWhqRkZFs376d\n7u5uYmNj8fl8xMfH88Mf/pBVq1bx5ZdfEhMTQ2xsLJWVlbS2thITE0N6ejoNDQ3YbDYCgQAA0dHR\nweW8//77BAIBYmJiUEoRGRlJXFwcra2ttLe309XVhc1mC+6TNpuNuLg4/H4/7e3t6LpOZ2cnPp8v\nuI2ioqJwu910d3eTkJCAYRhEREQwevRoqqqqaG1tpb6+Hp/Ph2ma2O123G43XV1d2O12UlJSMAyD\njo4ONE3D4/Hg9/sJDw8nISGBc845hw0bNtDQ0EBmZiaGYbB3715M0yQrKyv4usXHxzNixAicTmfw\nGDZ06FBWrVpFe3s7UVFRREREEBYWhtvtprm5GV3XcTgceL1eLBYLhYWFXH755XR3d7Njxw7a2trY\nsmULzc3NaJqGw+Ggvb0d0zSDw/Hx8QwfPpyYmBiGDRvGJZdcwujRo/8dh/DT3qnIvX4F/+rVq3nw\nwQdZuXIlQDCcf/GLXwTn+dGPfsSkSZO4+uqrASgsLKSkpIS9e/ces21hYSEffPABKSkp1NXVUVRU\nxLZt244s/t8c/Dt37uSC8ePpam7GB0QCA4CNQCKQqsEmBTlABaCABA3SdY3NhsKk5+8uoM1UGMBo\nm84mv4nSIN2q02EoOlCMDrOywWMQOLB+0RadPIeF0m4/BQ4ru7wGylRYdQigMTrSTrk3QKvfZGSk\nje3dAbpNRZRFoy2gGBJlZ7vbxwCnnYBS7Ovykx1hY1+XHwUMjwmjwRugwWuQH2Wn21DUewJ0BwxG\nJTqpcPto9xsoIM5hxRVpp7ShE13TKIwPpztgUtPpIzXCRkWHjxHJTqrdPtq9AUYmO/m8zk3AUIxz\nRbOzuRu3zyDaoeP2KRSKISmR1Lt9dPkMOrwBBiZH4guY7Hd76fQG0DSN0Vmx7G3sQgHREXYqmtzY\ndB2HTafLZ3BmXjybK9vQNY0BKZF8WdFKUqyDxnYfGfERxDhtbK9ux+s3KEiPxu0J4PEZdHT7SU2I\nIDbSwc6qNrz+AA6bhaTYCGKj7OyoaCVgKLLSorHoGvtq2sjNjMU0FXWNnXR3+8nMiKG5tZtuT4Ah\ng5LZtquB2JhwEhOc7NzdCCiUCVEx4aSlRbN9+35iYyNITY9h65ZaUAo0DYtFJys3Aa8nQMP+dhKS\no6ivbcdQJjablfyh6WzfWEkgYDJ4dBbVexrpbO/GYrMwYFg6OzdWYRiKvJGZNNW00tXhIeALkDUk\ng862Llr3t2EYJja7DVMpModnsu+LfZiGSWxaLB2NHWi6jmt4JpUby3HGR+Ju6iAhJxlN12ja10By\nfiq1W6vRLDoZZ+RSs3EvEQlRuBvaSSp0EfD4aC1vQAHpowZQt3EvpmEQP9BF07ZK0kYNoL2qka5m\nN6YysYc5cMQ4CU+KpqmsAnQd3WZBt1qJHZBO/YZdKMPEmZ6IZrHgrqrHHhOJZrfgb+8mwpUCSuHe\nV0PcsAG499VidHsIeH2g6ehWC/akeEDD29CELTYG5fMRkZdJ+8ZtWKKjMLu6sCUl4q9vJHLYIDq3\n7iRgKnRTYUtJwhIdQ/f2Hejh4dizs/Bs244l04VRXYM1PgFLYgLerVuxZWahvF78jQ3oNge2AQX4\ntm5CS0xB0y0YDXVgGGAqsFqwFAzDrNqHMvzg9aHlD0OVbwe/DwaMgMod4OkCNMgZDB0t0OWGrg60\nuDQ0exhmQwUYATRHBJaYNNA0Ag17saUMwuxqwexqQQX8aJqGPWkwvvoywhIHY3rb8btr0R1xYHjB\nVJj+LtCtYAaIjCnECHTi6arC4UjD66nB6cxHqQAeTx2m6UdTBrHhw/AEGvAbHTgs8XT769DQiHcM\no9GzgTA9GUO50RTEWQaxP7CeWC2XdlWBSYB0zqRZ38att93E7/545Ame6O1U5J61P42rq6vJzMwM\nDrtcLtauXXvceaqrq6mpqTlm2/3795OSkgJASkoK+/fv70+Zp8zcH/6Qs5ubeRtIAjbqGs8qCEPx\ntlXHomn8zTB5xlQM1jSqNfgw0o5V03jaZ/CEN8AeU/F5YgTfbvZwnkPn+047lzR2cVGEjYUJ4eRV\ntlOWF0eO3UKl32Dw7haSbDplQ5IJ1zXeavNwW1U7HxYmMmFrA+G6xl/zE7gm2YnfVBR9uZ+bM6K4\nLNHJiHXVtBkmi4Yl879N3VyYGMH8Ickopfjhxjper3MzKjaMq7NimVOQgGEqpn1UzrTMaG4flMg1\nH5djaPDSBQPwGSYDXtpCaqSdT64Ygt2ic8GrWzkzNZJHz8tBKcXN7+/m3fJWnpw2kGuHJuM3TC5c\n/iU3nZHOH5KcXPDsBlb9YAzegMmov66lzu1jWGoUM8/K4JbxWRimYsriddhsOm/PHt9T5/IvafcG\n+KyilY/vPB+P32DCox8S6bBi1SOZNDiJJ0v28sm8yYzJjae108cZ967kTzPHsLmylTlL1zPljHT+\ndc8kdF3jv/+1mVdWl+MNmOx68ntMue9tGt1eVi+5Cl3X+NOLG3nqzTJy0mJ4Zf40dF3jiRc3sGTF\nFlY/dy1zF6zi3LGZPHxHEUopfvG7Euob3XxRth+/3+TVZ65jXWk1b5fsZOlfr8Zi0Xnh5Q289K8v\n2bW7kb8snsGmL6t56aVSnn7lZmw2C2/8cwPz5xUTMEym3zieOXdfhFKKeXe8QmxiJDs217B5QxXP\nfHIXCSnRVOyq59Ypf+Th52bRUN3KnKmPs3T1L0hIjaFqdwM/mvR77n/5x4RHOrhhwN1c9YtLuPxn\nUzFNk0evWUTl1lo6mt3M3zSfmJQYarfX8quxv8Lv8aNbdOat/y0JWYk0ljfywOh7GHvdecxYeBOa\npvHKnc/idXs4b/YU3n+smDkf/ob9W6v404R7OPen32HKQ9ehlOLF7/8Be2wU3/7zf9FW2cBfRt5G\nwOPn8mU/Zdj08wj4/Dw59g66WrtIHJLJVa8/iG6x8MWiN9m8vITmbZVMe/FXZJw7gvJ3PqP46l9z\n9eaneSbjCgb/15W0bNqFMzMFnFGMWjAXpRRf/PS/sVg0Jr/1OG+M+T7RiXE0b9xB7JiRDP/zg3xy\n3gwGP/pLyp94irP/959YIsJp+mAdn8+4nRH/eprN03/I2A9fJjzbhae6jtVnTiNy4vnkLfkzmq6z\nf9GT7F/8N/JfeZmm55dT+5uHCTtjFJlLn0GzWGh5/lncK98i6ed3UXnrzaSv+F8sMTH4tm6m7qZr\nSHi7lPZf/hjvp6vQomMIv+9xbGdNxOxopeO7Z2B7/C30AcNQ7S34bpkItzwCiRlw61i45k6079yK\nMgx4+AaszmTMrZ/gnP8Jnr/PxSxbjaOwiKgZv0PTNNr/cTf4PMRNf4yGx6fh3/c5OT9eTf1b95Jw\n/gMkj70dpUz2vnwVHftKGHT1u+x5bQbOmOG4mz4nu/Cn5I94AKUUX376fVrrPyYn50cMHbKgZ9yX\nP6ah/l2GJv+EwSm3YyqDkp1XEOMoZFfTU0zPKyPcmkSzdwsr9k7AqaVzQ9x67FokVf6PeL3jKn5g\n/5ylvrO4hhVgwpK/Duea669izJgxX/eh/j9ev+7xa5p2QvOdyKcTpdRR+9M0rc/lzJs3L/ivpKTk\nhOo5WeV79xILeIAJQJSmsQ/FJF3DcqDGC3SNcgUxGlxk1bEeHG/VqTEVuRadRhOK7Ba6FZQHTMI1\njYvCbdQYihSrTo7dAkCmzUKmzcKwMBvhek8/k6IclHsNRkXYsGoaHhMuiA0DwKZrnB/joNwTINqq\nc2a0Hb9SXJgYQXm3nwuTnEDPNp2S5MQA6jwGk1N6LsdbdI3JKU7K3T40TeNb6dHo9CzXbtHJdNqY\nlBGN3dKz2/hMk4uzY4N9XuCKodkT4IID42wWnfMyYyhv7WZMWhSaBq2eABF2C2dnxpLktFPd7uHC\n/ITg8qcMTCQ+whbsc1JBz7T6Di8AYTYLZ+fFU9nSjakUKdHhWC0aY3LjAYh12hmdE095YyeThqSA\nBt8anY5+cPsNT6XLG6CyoROLRWfyGekkx0UEp59/Rjqd3QGmjMsMjisa7cIwe/bPyroOisZlB+s7\nd4wLf0BRW+/G4bAweGAyVTVtjDsrG8uB7TRhbDb7690U5CfR2Ohmz+5GJpyXj83W8zqPPScPwzCx\n2y2MPWdAsO/x5xdQV9VKTHw4rgFJJKREA5CVn0xMgpOW+g5aG9248pNISI0BwDUgibjkKFrq2rBY\nLaAUwyf13HrTdZ0zJg9F1zRsdhsxKT1t0galERYdRmJ2Ikm5ySRkJQKQmJ2Iw+mgcPLw4HtwYNEQ\nmssbKJw0DHdDOwApg11Y7FYGTB4ZrL3g4tF4Wg/cWslMIn5AGh2VDeReMAIAq91G7uQzsIbZyJo4\nAt3Ssy2yLxyJu7qR5NH5dNW19KzTpFH4OroIdHRjBgxQitTzR+Gu2E9K0ZnBZaYUnUVnRR02ZzhJ\nE0YQ6PaARSdpyrl46hoIy87A8HiIPXMElohwAOLPHYPZ7QUNHBmphGe7evazjFT08AiiJ56Hpve8\njlHnjEcF/CjDIPLsCSjTxHnueWgHandOOBt/dTWB2hocg4dhienZvvbBw8Cig7sD+1nngFKolkas\no84BAE83OMLRBwzrWZfoOLQBw6G+Ei06HnQdzijqmWaxwIhz0Gx2zMbKnm054kKU4cNeODH4OtmH\nTMJorkDTLdizz0R3ROJIHkygtYKo7AN9aTpRORegWR0Y3Y0408aiWyzoFgfxqRcEt2ti2sUo009S\n4oX/Ny5pEobZRVr05J59S7OQEn0+7Z7txDuGEW5N6tm+jqFY9UgSrcOwaz3HmQzruXSrJmL0LCJJ\npYNawokjmWGUl5cjeispKemVc6dCv4L/4P3ZgyorK3G5XH3OU1VVhcvlOur4jIwMgOAlfoDa2lqS\nk5OPWcOhG6SoqKg/q3NcZ44fzz6LhXDgbWCnUpylaTxrKBqVQinFnw3FaB3KleJpn0GDeWC8N0C+\nRafCMHFq8Io3gI7iDLsFt6lY3O4l2aLTEDBZ1ekD4KMuPxV+g0/cXip8BgB/buhkjNPGC83doBR2\nDRZWt6OUYr/P4MWGLsZEOdjR5WdViwebpvHn8lbGxDhYvK8Vn6noCpj8tbwVp0UnN8LKH3c0YipF\ni89g2b5WzogLx+03WLyzCbffRClFbZefbW0e/rGzibpOX8+HOQWPb6jFb5h0+Q2e2lJPTnQYj39e\n3VNPp48XtzYwJi2a5zbvx2HViQ+3sq+lmzd3NFLb4WVQopOFn/Q8m9DU6eOZ9dXsberCb5h0egMs\nW1dFpy9AZlzPgbqyuYvXv6xjdHYM/oBJaXnPcw7Pf7IPgLKqNj7a3sDwzBieeGcHVovGX9/eQXuX\nD8MwWbRyO3arzqgB8TS1e3h21S52V7fR5vZiGCZ/e72MmEg7S18vo7WjZ9xf/7UZ01R0dvsZOSiR\nv7+0Aa8vgMcb4PnXt2CaJkMHJmHRdd58dzsjh6by2ptbaG7pQinF/7zwBTlZcZRt3U9cbARjzsri\n9X9uoKnRjVKKF55ei67r+DwBXnl2HX6/QXe3j1eeXUv+4FT27W6kfMd+tn5RAcDqd8roaO0mOSOW\niKgwyrfvZ+vnPQfMte9tpa2pk6TMeFobevaLtxb9L4Zh0tXezXtPfYTfH8Dn8bHn8z0AbCjegN8T\noHZ7LY3lDWz/sOf++7YPyvB1efnor+/i9/jwe/188vdVZI7OZdXjbxGX0/O+3PL6ZyjTZM3CYgx/\nAF+nh7V/eQtHTAQA5R9tpnl3LSmj81m78A2UUnTUtbB5+Qd427ooe34V3c0dKNPkiz+/QdzADGo+\n2UJYQs8HnY0L/4UjNhIFhCXFEujysucf7xE7JJc9T72K4fVheLzs+vs/iR81iI491VSv/BRLmB1d\n16lc9gqOxHg8lTUANLz3MV37qntq+9uLWCIj8NY14KtvovnDnquOravXY3Z30fTcCxgdbpRh0PD0\ns+jhEaBpND39DHpEBG0vv4jR2ooyTVr+52nChg3D5nLhKf0M387tAHS+9RpauBNltdL92j/AYkFL\nceH911IAlM8Dfh/Gh68DYO7Zgir7DHKGoPZugUAAVvwVZZoodyusehnV3oyeOxL8XnzvPIlmddD9\nyTMovwfl99JV8iQ21xkYnU10f/kGpq+bjq2v48gYQ8MXi1GmQcDTStPGZaiAB93mpL38PfzeFsxA\nF1U7/4pp+gkEOqnc+Vesthj27vsLpunDMLqpqFiK3ZbA1v1/QikTb6CFvU3LSXJOoMGznkZPz0Pc\n+zpeBRTV/k9oNXYD8KVnCfHaICrMD+iigViy2c9mavic4cOH9/s4/Z+mqKjolAd/v+7xBwIBBg0a\nxPvvv096ejpjx47t8+G+NWvWMHfuXNasWdNn27vuuouEhATuvvtu5s+fT2tr6zfi4b6WlhauuPhi\n1n32GSZgAo4D//UBdkADDMByYHzgkPE+ej5pBQ781wroGnQpCNfA15OlWDSwaxo+pTBVT1tTgzBN\nw0ShqZ5hn9kzza5raBp4TYVN07Ac+FsHNAUWy4HtpGmYqqcuuwamqQgA1gNntj5T4bBoBEyFQsOu\n99yK1DUNj6nQUFh0nYCpCLNomAeu0hgKTKWwaBqmMrFZdJQCr6Gw6D1XCwKGwkRh03U8AROrrmEo\nBUoRZrNgKPAZJg5LTy09fYLNomEe2AgWTccTMLDoOmgaOib6gXF2i47VouHxm5imwnHgbDpg9swf\nMBRWi4ZF7+nPBAKGwm7VUUodmK5jsWj4AwbQM5/VqqPrGqZpEjB6Xi+rVccfMAGwWXUMU6EU+AMG\ndpsFXdcwDEXAMLHbLGi6hs8X4OCu6nBYCRjmgbN8a09bnx/QsNktPfUdWHYgYGKx6Jhmz1Uxu8NK\nwG+glMJqs+DzBkApNIuOzd4zDa3n7N7vC6BbNKzWnj6NgIHFZkUpE78ngMVmweawEfAHUKZC03UM\nfwCL1YLVYcXvCQAKi92K4TPQNNAsPdtL1zX8vgD2MDuG38BUCqvNihkwME2FxapjBAysDjsBr7/n\neRTHgTuLmkbA40Oz6GiWnp3MDJhY7FY0vWcaes94S5i9J/BMExUw0aw6oKFZdAyPD0uYAzMQAAW6\nzQooTK8fbJaefdPrQ7faUIbRc+auaWDRUT4/usMBysTwBdB0rWe6qdDsNpTPh+nzo4WFQSCAZrWC\nrmN6PD3ttJ59QgOUP4Bmt4Gm9VyKN4wDRwwNzWGHgIEyTVAmWGzg84DNDrqlpx6fFzS9Z50t1p7p\naGB3gN/b8/yH1d7zX8MPFjugwAhw4EUB00Sz2FCGr2ecbgXTBPPA/L5ONGs46FY0pVCYYAbQdBum\n4UdDodDRdStmoBuLNQKlDJQy0TQrpuHHYnWgTD+g0DQ7htGNVQ9DoVDKj4YVUwXQNL1nv9EcmMoP\nykTRs/NbcWBioKGhMFAorDjAGuCpZX/j2uuuOQVH6v9sX/vDfQBvvfUWc+fOxTAMZs2axT333MPi\nxYsBuPXWWwGYM2cOK1euxOl0snTp0uDTm0drCz1f55s+fToVFRXk5OTw4osvEhsbe2TxX8NT/Uop\n6uvraWlpYfXq1URHR5OXl0dpaSm6rpOVlcXWrVsJDw/nnHPOIT09naamJmpra7Hb7VRWVpKQkEBO\nTg5xcXFs2LAB0zRJTU3lgw8+IDMzk8TEREpLS2lsbMThcFBUVITP5yMmJoaKigrq6uoYM2YM5eXl\nOBwOEhMTg08BezweBg8ejMvl4rPPPgs+gf3RRx8xatQoPB4Pdrsdl8vFnj17OOOMM/B6vXzyySdE\nRUURCASIjY1F13V2796NxWIhLy8Pp9NJXV0dVVVV5Obm0t7eTm1tLSNHjqS5uZnY2Fjsdjtbt27F\n7/fjdDpxuVxYrVa8Xi/p6elERESwb98+EhISCA8PZ/v27QwcOJDy8nI6OztpbGykqakJm81GRkYG\nBQUFVFRUEB8fT3h4ePDJaqfTidVqxW63s23bNvbs2cPAgQMpKytj6NChtLS0EBERQWVlJZGRkWRn\nZ7N+/Xra2tpwOBxERESQm5tLW1sbVquVkSNHsn//fmw2G+Xl5cTFxREbG8uWLVswDAOv18vEiRP5\n8MMPiY+PJykpib179+LxeAAYOHAgW7ZsISkpie7ubmw2G8OHD6elpYU9e/ZgmiZ5eXlkZGTw8ccf\ns23bNhwOB0lJST0fKAIBlFKkpaXR0dFBWFgYBQUFbN++HY/Hw7e+9S2SkpLYtGkT69evZ+zYsZSX\nl1NaWkpMTAzTpk1D13Vqamqoqalh06ZNmKZJbm4uycnJJCUl8cUXX5CTk0NqaiotLS0MHTqU3bt3\nU1NTQ3JyMq2trZSVlTFw4ECysrIoLS2ls7OT2NhYoqOj8Xg8dHZ2opTCYrGQlpZGQkICFRU9VyG6\nurqCT6vX19czcuRIcnNzaWho4J133qG5uZnc3FwmTpxIXV0dO3bsIDk5maqqKlJTUzFNk+HDh+P1\nevn000+DVwB1XWfQoEFomkZDQwOtra2MGzeOHTt2EBERwYoVKxg9ejQOh4OMjAw+++wzqqqqGD9+\nPNu3b2fQoEFMmDCB5uZmVqxYwfjx4wkEAtTV1bFv3z5ycnLIyspiz549wW9VdHd3Ex0dTUZGBmFh\nYbzxxhvU1NRw9tlnU1tbS1ZWFjExMVRVVfH/2rv/2KjvOo7jr6t0ijJW19HrT1IGLW3p+mOUgkvm\nOsuBMDEbIiICjTD+mBIDLLTwj4IRuG4h0UkimmiGc6liSICM0qwDbm4RLBsobq0UB7XttVcn5TYH\no9Drxz8mDdD2ety113af5yO5hO/3Pu+79ztf4MX3+r0vDodDTU1NiomJUX5+vi5cuND7DZyenh55\nvV7Fx8fL5/Pp8uXLSkpK0mc+8xnFxcUpEAjo3LlzeuSRR9Ta2qq4uDjl5OTI6/Wqu7tb//znPzV+\n/HhdunRJCQkJev/991VfX6/ExEQVFhYqEAjo/PnzSk5O1vnz5/Wf//xHM2bM0IQJE1RaWqq///3v\nOn/+vGbNmqUPP/xQFy5ckNfr1aJFi9TQ0KB//etfys7OVnp6uuLi4lRfX6/r16+roKBAp06d0vHj\nx/X444+rp6dH9957r7q6unTq1Cl99rOfVUZGhhobG/WFL3xBc+bMUVFRkTo6OuRwOHq/lfCXv/xF\nEydOVFJSkt555x29++67SkxMVHZ2tpxOpwoKCiRJ8fHxmjx5sj73uc9F9e/ysWpUBP9IGongBwBg\npAxF7nHnPgAALELwAwBgEYIfAACLEPwAAFiE4AcAwCIEPwAAFiH4AQCwCMEPAIBFCH4AACxC8AMA\nYBGCHwAAixD8AABYhOAHAMAiBD8AABYh+AEAsAjBDwCARQh+AAAsQvADAGARgh8AAIsQ/AAAWITg\nBwDAIgQ/AAAWIfgBALAIwQ8AgEUIfgAALELwAwBgEYIfAACLEPwAAFiE4AcAwCIEPwAAFiH4AQCw\nCMEPAIBFIgr+zs5OuVwuZWZmat68efL7/f2uq6mpUVZWljIyMlRZWTlofW1trYqKipSXl6eioiId\nP348kjYBAMD/RRT8brdbLpdLjY2NKi0tldvt7rMmEAho3bp1qqmpUX19vaqqqtTQ0BC0ftKkSXrl\nlVd09uxZ7d27VytXroykTQAA8H8OY4wJtzgrK0uvv/66nE6nfD6fSkpK9I9//OO2NSdOnNC2bdtU\nU1MjSb3hvnnz5pDqjTF64IEH5PP5FBsbe3vzDociaB8AgDFlKHIvojP+jo4OOZ1OSZLT6VRHR0ef\nNV6vV2lpab3bqamp8nq9Idfv379fM2fO7BP6AADg7o0bbIHL5ZLP5+uzf/v27bdtOxwOORyOPuvu\n3GeMGXDdnfvfffddbd68WbW1tYO1CQAAQjBo8AcL3Zsf0ScmJqq9vV0JCQl91qSkpKilpaV3u7W1\nVSkpKYPWt7a2avHixXrppZc0ZcqUAXvYunVr769LSkpUUlIy2EgAAIwJHo9HHo9nSF8zop/xl5eX\nKz4+XhUVFXK73fL7/X0u8Ovu7tb06dN19OhRJScnq7i4WFVVVcrOzh6w3u/367HHHtO2bdv05JNP\nDtw8P+MHAFhkKHIvouDv7OzU0qVL1dzcrPT0dO3bt09xcXFqa2vT2rVrdfjwYUnSkSNHtH79egUC\nAa1Zs0ZbtmwJWv+Tn/xEbrdbGRkZve9VW1urBx544PbmCX4AgEVGPPhHGsEPALDJiF/VDwAAxhaC\nHwAAixD8AABYhOAHAMAiBD8AABYh+AEAsAjBDwCARQh+AAAsQvADAGARgh8AAIsQ/AAAWITgBwDA\nImT3m74AAA/NSURBVAQ/AAAWIfgBALAIwQ8AgEUIfgAALELwAwBgEYIfAACLEPwAAFiE4AcAwCIE\nPwAAFiH4AQCwCMEPAIBFCH4AACxC8AMAYBGCHwAAixD8AABYhOAHAMAiBD8AABYh+AEAsAjBDwCA\nRQh+AAAsQvADAGCRsIO/s7NTLpdLmZmZmjdvnvx+f7/rampqlJWVpYyMDFVWVoZc39zcrAkTJmjX\nrl3htggAAO4QdvC73W65XC41NjaqtLRUbre7z5pAIKB169appqZG9fX1qqqqUkNDQ0j1Gzdu1BNP\nPBFuewAAoB9hB/+hQ4dUVlYmSSorK9OBAwf6rKmrq9O0adOUnp6u2NhYLVu2TAcPHhy0/sCBA3rw\nwQeVk5MTbnsAAKAfYQd/R0eHnE6nJMnpdKqjo6PPGq/Xq7S0tN7t1NRUeb3eoPUfffSRnnvuOW3d\nujXc1gAAwADGBXvS5XLJ5/P12b99+/bbth0OhxwOR591d+4zxgy47ub+rVu3asOGDfr85z8vY8zg\nEwAAgJAFDf7a2toBn3M6nfL5fEpMTFR7e7sSEhL6rElJSVFLS0vvdmtrq1JSUoLW19XVaf/+/Sov\nL5ff71dMTIzGjx+v733ve/32cesnAyUlJSopKQk2EgAAY4bH45HH4xnS13SYME+ry8vLFR8fr4qK\nCrndbvn9/j4X6HV3d2v69Ok6evSokpOTVVxcrKqqKmVnZ4dUv23bNt17773auHFj/807HHwqAACw\nxlDkXtg/49+8ebNqa2uVmZmpY8eOafPmzZKktra23qvxx40bp927d2v+/PnKycnRt771LWVnZwet\nBwAAwyfsM/7RgDN+AIBNRvSMHwAAjD0EPwAAFiH4AQCwCMEPAIBFCH4AACxC8AMAYBGCHwAAixD8\nAABYhOAHAMAiBD8AABYh+AEAsAjBDwCARQh+AAAsQvADAGARgh8AAIsQ/AAAWITgBwDAIgQ/AAAW\nIfgBALAIwQ8AgEUIfgAALELwAwBgEYIfAACLEPwAAFiE4AcAwCIEPwAAFiH4AQCwCMEPAIBFCH4A\nACxC8AMAYBGCHwAAixD8AABYhOAHAMAiYQd/Z2enXC6XMjMzNW/ePPn9/n7X1dTUKCsrSxkZGaqs\nrAyp/uzZs/rSl76k3Nxc5eXlqaurK9w2AQDALcIOfrfbLZfLpcbGRpWWlsrtdvdZEwgEtG7dOtXU\n1Ki+vl5VVVVqaGgIWt/d3a2VK1fqV7/6ld555x29/vrrio2NDbdNAABwi7CD/9ChQyorK5MklZWV\n6cCBA33W1NXVadq0aUpPT1dsbKyWLVumgwcPBq1/9dVXlZeXp4ceekiS9MUvflExMfxEAgCAoRB2\nonZ0dMjpdEqSnE6nOjo6+qzxer1KS0vr3U5NTZXX6w1a39jYKIfDoa9+9auaOXOmnn/++XBbBAAA\ndxgX7EmXyyWfz9dn//bt22/bdjgccjgcfdbduc8YM+C6m/u7u7v15ptv6q233tL48eNVWlqqmTNn\n6itf+crg0wAAgKCCBn9tbe2AzzmdTvl8PiUmJqq9vV0JCQl91qSkpKilpaV3u7W1VSkpKUHr09LS\n9OUvf1n333+/JGnhwoU6ffr0gMG/devW3l+XlJSopKQk2EgAAIwZHo9HHo9nSF/TYYwx4RSWl5cr\nPj5eFRUVcrvd8vv9fS7w6+7u1vTp03X06FElJyeruLhYVVVVys7OHrD+8uXLmjt3rt58803FxsZq\nwYIF2rhxoxYsWNC3eYdDYbYPAMCYMxS5F3bwd3Z2aunSpWpublZ6err27dunuLg4tbW1ae3atTp8\n+LAk6ciRI1q/fr0CgYDWrFmjLVu2BK2XpJdfflk7d+6Uw+HQE0880e83BiSCHwBglxEN/tGA4AcA\n2GQoco/vyQEAYBGCHwAAixD8AABYhOAHAMAiBD8AABYh+AEAsAjBDwCARQh+AAAsQvADAGARgh8A\nAIsQ/AAAWITgBwDAIgQ/AAAWIfgBALAIwQ8AgEUIfgAALELwAwBgEYIfAACLEPwAAFiE4AcAwCIE\nPwAAFiH4AQCwCMEPAIBFCH4AACxC8AMAYBGCHwAAixD8AABYhOAHAMAiBD8AABYh+AEAsAjBDwCA\nRQh+AAAsQvADAGCRsIO/s7NTLpdLmZmZmjdvnvx+f7/rampqlJWVpYyMDFVWVg5af+3aNX37299W\nXl6ecnJy5Ha7w20RAADcIezgd7vdcrlcamxsVGlpab8BHQgEtG7dOtXU1Ki+vl5VVVVqaGgIWv/7\n3/9eknT27Fm9/fbb+uUvf6nm5uZw2xyzPB7PSLcwrJhvbGO+sevTPJv06Z9vKIQd/IcOHVJZWZkk\nqaysTAcOHOizpq6uTtOmTVN6erpiY2O1bNkyHTx4MGh9UlKSrly5okAgoCtXruiee+7RxIkTw21z\nzPq0/+ZlvrGN+cauT/Ns0qd/vqEQdvB3dHTI6XRKkpxOpzo6Ovqs8Xq9SktL691OTU2V1+sNWj9/\n/nxNnDhRSUlJSk9P16ZNmxQXFxdumwAA4Bbjgj3pcrnk8/n67N++fftt2w6HQw6Ho8+6O/cZYwZc\nd3P/7373O3388cdqb29XZ2enHn30UZWWlmrKlCmDTwMAAIIzYZo+fbppb283xhjT1tZmpk+f3mfN\niRMnzPz583u3d+zYYdxud9D6Z555xrz00ku9NatXrzb79u3rtwdJPHjw4MGDh1WPSAU94w/m61//\nuvbu3auKigrt3btXTz75ZJ81RUVFOn/+vJqampScnKw//OEPqqqqClqflZWlY8eOacWKFbpy5YpO\nnjypDRs29NvDJ9kPAABC5TBhpmdnZ6eWLl2q5uZmpaena9++fYqLi1NbW5vWrl2rw4cPS5KOHDmi\n9evXKxAIaM2aNdqyZUvQ+q6uLq1Zs0Z/+9vf1NPTo9WrV+vZZ58duokBALBY2MEPAADGnlF9575I\nbxJUV1en4uJiFRYWatasWTp16lS0Wg9JpPNJ0s9//nNlZ2crNzdXFRUV0Wg7ZEMxnyTt2rVLMTEx\n6uzsHO6W70qk823atEnZ2dnKz8/X4sWL9cEHH0Sr9QENdiwk6Qc/+IEyMjKUn5+vM2fO3FXtSAt3\nvpaWFj3++OOaMWOGcnNz9cILL0Sz7ZBFcvykT+69UlhYqEWLFkWj3bsWyXx+v19LlixRdna2cnJy\ndPLkyWi1HZJIZtu5c6dmzJihhx56SMuXL1dXV1fwN4v4KoFhtGnTJlNZWWmMMcbtdpuKioo+a7q7\nu83UqVPNxYsXzfXr101+fr6pr683xhjz2GOPmZqaGmOMMdXV1aakpCR6zYcg0vmOHTtm5s6da65f\nv26MMebf//539JoPQaTzGWNMc3OzmT9/vklPTzeXLl2KWu+hiHS+V1991QQCAWOMMRUVFf3WR9Ng\nx8IYYw4fPmwWLFhgjDHm5MmTZvbs2SHXjrRI5mtvbzdnzpwxxhjz3//+12RmZn6q5rtp165dZvny\n5WbRokVR6ztUkc63atUq8+tf/9oYY8yNGzeM3++PXvODiGS2ixcvmilTpphr164ZY4xZunSpefHF\nF4O+36g+44/0JkFJSUm9Z1F+v18pKSnRaz4Ekc73i1/8Qlu2bFFsbKwkadKkSdFrPgSRzidJGzdu\n1HPPPRe1nu9GpPO5XC7FxHzyR3D27NlqbW2NXvP9GOxYSLfPPHv2bPn9fvl8vpBqR1q483V0dCgx\nMVEFBQWSpAkTJig7O1ttbW1RnyGYSOaTpNbWVlVXV+vpp58elRdORzLfBx98oDfeeEOrV6+WJI0b\nN0733Xdf1GcYSCSzTZw4UbGxsbp69aq6u7t19erVQbNuVAd/pDcJcrvdevbZZzV58mRt2rRJO3fu\njE7jIYp0vvPnz+tPf/qT5syZo5KSEr311lvRaTxEkc538OBBpaamKi8vLzoN36VI57vVb37zGy1c\nuHD4mg1BKL0OtKatrS2kOUdSuPPd+Q+ypqYmnTlzRrNnzx7ehu9SJMdPkjZs2KDnn3++9x+jo00k\nx+/ixYuaNGmSvvvd7+rhhx/W2rVrdfXq1aj1PphIjt3999/fm3PJycmKi4vT3Llzg75f2F/nGypD\nfZOgW61Zs0YvvPCCnnrqKf3xj3/U6tWrVVtbG3nTd2E45+vu7tbly5d18uRJnTp1SkuXLtWFCxci\nb/ouDNd8H3/8sXbs2HHb8RqJs5DhPH63vtY999yj5cuXh9/oEAilV2nsfo023Plurfvoo4+0ZMkS\n/exnP9OECROGtL9IhTufMUavvPKKEhISVFhYOGpveRvJ8evu7tbp06e1e/duzZo1S+vXr5fb7daP\nf/zj4Wj1rkXyZ++9997TT3/6UzU1Nem+++7TN7/5Tb388sv6zne+M+DrjHjwBwtip9Mpn8+nxMRE\ntbe3KyEhoc+alJQUtbS09G63tLQoNTVV0icfn7z22muSpCVLlujpp58e4u4HN5zzpaamavHixZKk\nWbNmKSYmRpcuXVJ8fPwQTzGw4ZrvvffeU1NTk/Lz8yV98jHkzJkzVVdX1+/rDJfhPH6S9OKLL6q6\nulpHjx4d2sbDMFiv/a1pbW1Vamqqbty4MWjtSAt3vpsfm964cUPf+MY3tGLFin7vWzLSIplv//79\nOnTokKqrq3Xt2jV9+OGHWrVqlX77299Grf/BRDKfMUapqamaNWuWpE/yYDT9z6+RzObxePTII4/0\n/r2/ePFi/fnPfw4a/KP+4r6bd/rbuXNnvxc/3bhxwzz44IPm4sWLpqur67aLIgoLC43H4zHGGPPa\na6+ZoqKi6DUfgkjn27Nnj/nhD39ojDHm3LlzJi0tLXrNhyDS+W41Wi/ui2S+I0eOmJycHPP+++9H\nte+BhHIsbr3A6MSJE70XGIV6HEdSJPP19PSYlStXmvXr10e971BFMt+tPB6P+drXvhaVnu9GpPM9\n+uij5ty5c8YYY370ox+Z8vLy6DU/iEhmO3PmjJkxY4a5evWq6enpMatWrTK7d+8O+n6jOvgvXbpk\nSktLTUZGhnG5XOby5cvGGGO8Xq9ZuHBh77rq6mqTmZlppk6danbs2NG7/9SpU6a4uNjk5+ebOXPm\nmNOnT0d9hmAine/69etmxYoVJjc31zz88MPm+PHj0R4hqEjnu9WUKVNGXfBHOt+0adPM5MmTTUFB\ngSkoKDDPPPNM1Ge4U3+97tmzx+zZs6d3zfe//30zdepUk5eXZ95+++2gtaNNuPO98cYbxuFwmPz8\n/N7jdeTIkRGZIZhIjt9NHo9nVF7Vb0xk8/31r381RUVFJi8vzzz11FOj6qp+YyKbrbKy0uTk5Jjc\n3FyzatWq3m96DYQb+AAAYJHRefkmAAAYFgQ/AAAWIfgBALAIwQ8AgEUIfgAALELwAwBgEYIfAACL\nEPwAAFjkf27hYOpjUwj4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108f6d2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.manifold import locally_linear_embedding\n",
    "\n",
    "X_lle, err = locally_linear_embedding(X, n_neighbors=12, n_components=1)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X_lle, np.zeros((800,1)), c=color, cmap=plt.cm.rainbow)\n",
    "\n",
    "plt.title('First principal component after Locally Linear Embedding')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Appendix A: Projecting new data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, so good, in the sections above, we have been projecting an dataset onto a new feature subspace. However, in a real application, we are usually interested to map new data points onto the same new feature subspace (e.g., if are working with a training and a test dataset in pattern classification tasks).\n",
    "\n",
    "Remember, when we computed the eigenvectors \\\\( \\mathbf{\\alpha} \\\\) of the centered kernel matrix, those values were actually already the projected datapoints onto the principal component axis \\\\( \\mathbf{g} \\\\). \n",
    "\n",
    "If we want to project a new data point \\\\( \\mathbf{x} \\\\) onto this principal component axis, we'd need to compute \\\\(\\phi(\\mathbf{x})^T  \\mathbf{g} \\\\).\n",
    "\n",
    "Fortunately, also here, we don't have to compute \\\\(\\phi(\\mathbf{x})^T  \\mathbf{g} \\\\) explicitely but use the kernel trick to calculate the RBF kernel between the new data point and every data point \\\\( j \\\\) in the training dataset:\n",
    "\n",
    "$$\\phi(\\mathbf{x})^T  \\mathbf{g}  = \\sum_j \\alpha_{i} \\; \\phi(\\mathbf{x}) \\; \\phi(\\mathbf{x_j})^T$$\n",
    "\n",
    "$$=  \\sum_j \\alpha_{i} \\; \\kappa(\\mathbf{x}, \\mathbf{x_j})$$\n",
    "\n",
    "\n",
    "and the eigenvectors \\\\( \\alpha \\\\) and eigenvalues \\\\( \\lambda \\\\) of the Kernel matrix \\\\(\\mathbf{K}\\\\) satisfy the equation\n",
    "\\\\(\\mathbf{K} \\alpha = \\lambda \\alpha \\\\), we just need to normalize the eigenvector by the corresponding eigenvalue.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let us modify our original implemenation by returning the corresponding to return also the eigenvalues of the kernel matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.spatial.distance import pdist, squareform\n",
    "from scipy import exp\n",
    "from scipy.linalg import eigh\n",
    "import numpy as np\n",
    "\n",
    "def stepwise_kpca(X, gamma, n_components):\n",
    "    \"\"\"\n",
    "    Implementation of a RBF kernel PCA.\n",
    "    \n",
    "    Arguments:\n",
    "        X: A MxN dataset as NumPy array where the samples are stored as rows (M),\n",
    "           and the attributes defined as columns (N).\n",
    "        gamma: A free parameter (coefficient) for the RBF kernel.\n",
    "        n_components: The number of components to be returned.\n",
    "        \n",
    "    Returns the k eigenvectors (alphas) that correspond to the k largest \n",
    "        eigenvalues (lambdas).\n",
    "    \n",
    "    \"\"\"\n",
    "    # Calculating the squared Euclidean distances for every pair of points\n",
    "    # in the MxN dimensional dataset.\n",
    "    sq_dists = pdist(X, 'sqeuclidean')\n",
    "\n",
    "    # Converting the pairwise distances into a symmetric MxM matrix.\n",
    "    mat_sq_dists = squareform(sq_dists)\n",
    "\n",
    "    # Computing the MxM kernel matrix.\n",
    "    K = exp(-gamma * mat_sq_dists)\n",
    "\n",
    "    # Centering the symmetric NxN kernel matrix.\n",
    "    N = K.shape[0]\n",
    "    one_n = np.ones((N,N)) / N\n",
    "    K_norm = K - one_n.dot(K) - K.dot(one_n) + one_n.dot(K).dot(one_n)\n",
    "    \n",
    "    # Obtaining eigenvalues in descending order with corresponding \n",
    "    # eigenvectors from the symmetric matrix.\n",
    "    eigvals, eigvecs = eigh(K_norm)\n",
    "\n",
    "    # Obtaining the i eigenvectors (alphas) that corresponds to the i highest eigenvalues (lambdas).\n",
    "    alphas = np.column_stack((eigvecs[:,-i] for i in range(1,n_components+1)))\n",
    "    lambdas = [eigvals[-i] for i in range(1,n_components+1)]\n",
    "    \n",
    "    return alphas, lambdas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's make a new half-moon dataset and project it onto a 1-dimensonal subspace using the RBF kernel PCA:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sebastian/miniconda3/envs/py34/lib/python3.4/site-packages/sklearn/datasets/samples_generator.py:612: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "  y = np.hstack([np.zeros(n_samples_in, dtype=np.intp),\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "X, y = make_moons(n_samples=100, random_state=123)\n",
    "alphas, lambdas = stepwise_kpca(X, gamma=15, n_components=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To confirm that our approach produces the correct results, let's pretend that the 24th point from the half-moon dataset is a new data point  \\\\( \\mathbf{x} \\\\), and we want to project it onto this new subspace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x_new = X[25]\n",
    "X_proj = alphas[25] # original projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.8713187 ,  0.00928245])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.07877284])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_proj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def project_x(x_new, X, gamma, alphas, lambdas):\n",
    "    pair_dist = np.array([np.sum((x_new-row)**2) for row in X])\n",
    "    k = np.exp(-gamma * pair_dist)\n",
    "    return k.dot(alphas / lambdas)\n",
    "\n",
    "# projection of the \"new\" datapoint\n",
    "x_reproj = project_x(x_new, X, gamma=15, alphas=alphas, lambdas=lambdas) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.07877284])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_reproj "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NrNLMOiTbThEREUky+M0sDbgPKAL6AiPN7KhqZYYCR7h7b+BK4IFE6ppZN+B0\noDSZNoqIiMheyY74BwLL3X2Fu5cDTwJnVyszDHgMwN3fBrLMLDeBur8BbkiyfSIiIhIl2eDPB1ZG\nTZeF5yVSJq+mumZ2NlDm7ouSbJ+IiIhESU+yvidYzhJdoZm1Bn5J6DR/veuLiIhIzZIN/lVAt6jp\nboRG7rWV6Rouk1FD3V5AD2ChmVWVf8/MBrr7uuoNKC4ujjwvLCyksLCwQR0RERFpakpKSigpKUnp\nOs090UF7nMpm6cBS4FRgNbAAGOnui6PKDAXGuftQMxsE3OvugxKpG67/OXCcu2+Ms31Ppv0iIiLN\niZnh7kmdBU9qxO/uFWY2DngFSAMedvfFZnZVePlD7v6SmQ01s+XANmBsbXXjbSaZNoqIiMheSY34\nG5tG/CIiEiSpGPHrzn0iIiIBouAXEREJEAW/iIhIgCj4RUREAkTBLyIiEiAKfhERkQBR8IuIiASI\ngl9ERCRAFPwiIiIBouAXEREJEAW/iIhIgCj4RUREAkTBLyIiEiAKfhERkQBR8IuIiASIgl9ERCRA\nFPwiIiIBouAXEREJEAW/iIhIgCj4RUREAkTBLyIiEiAKfhERkQBR8IuIiASIgl9ERCRAFPwiIiIB\nouAXEREJEAW/iIhIgCj4RUREAkTBLyIiEiAKfhERkQBR8IuIiASIgl9ERCRAFPwiIiIBknTwm1mR\nmS0xs2VmdmMNZaaFly80s/511TWzKWa2OFz+WTNrn2w7RUREJMngN7M04D6gCOgLjDSzo6qVGQoc\n4e69gSuBBxKo+ypwtLt/B/gEuCmZdoqIiEhIsiP+gcByd1/h7uXAk8DZ1coMAx4DcPe3gSwzy62t\nrru/5u6V4fpvA12TbKeIiIiQfPDnAyujpsvC8xIpk5dAXYBLgZeSbKeIiIiQfPB7guWsISs3s5uB\n3e7+eEPqi4iISKz0JOuvArpFTXcjNHKvrUzXcJmM2uqa2SXAUODU2hpQXFwceV5YWEhhYWGCTRcR\nEWnaSkpKKCkpSek6zT3RQXucymbpwFJC4bwaWACMdPfFUWWGAuPcfaiZDQLudfdBtdU1syJgKjDE\n3TfUsn1Ppv0iIiLNiZnh7g06i14lqRG/u1eY2TjgFSANeDgc3FeFlz/k7i+Z2VAzWw5sA8bWVje8\n6v8BDgFeMzOA+e5+TTJtFRERkSRH/I1NI34REQmSVIz4dec+ERGRAFHwi4iIBIiCX0REJEAU/CIi\nIgGi4BdnLuxGAAAWgElEQVQREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0RE\nJEAU/CIiIgGi4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0REJEAU/CIi\nIgGi4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4jsZ5t2bGL+yvkpX+/8lfPZtGNT\nytcrBzcFv4jIfrZkwxKGPTmMkhUlKVtnyYoShj05jCUblqRsnRIMCn4Rkf1scLfBzB4+m+Gzh6ck\n/EtWlDB89nBmD5/N4G6Dk2+gBIqCX0TkACjsUZiS8I8O/cIehSlrnwSHgl9E5ABJNvwV+pIKCn4R\nkQOooeGv0JdUUfCLiBxgtYX/hx9+yIcffhgzT6EvqWTu3thtaDAz8+bcfhEJtuqB7u706dMHM2Pp\n0qWYmUJfYpgZ7m7JrCPpEb+ZFZnZEjNbZmY31lBmWnj5QjPrX1ddM+tgZq+Z2Sdm9qqZZSXbThGR\npqb6yH/OnDl8+eWXrFmzhhdeeEGhL/tFUiN+M0sDlgKnAauAd4CR7r44qsxQYJy7DzWz44Hfufug\n2uqa2WRgg7tPDr8hyHb38XG2rxF/tClTYNo0+PprOPRQyMqC/Hzo1w/c4fPPQ+UOPxw6dAAz2LAh\n9PjWt2DwYJg/H5YuhSOPhEGD4K23YMmS0PILLgjVf/LJvWXOPz807403YN260HY6dw5t47PP9m6v\n6vnJJ+8tv3ZtqA05ObHza6tT32VHHAHLlze8LtRev671V19efZuJriORdlSVeeqp2H1WtSxa9TbF\nK5MiiWyqqkz1X4mG7IKGvsSpXkd9lrfpW8JP3xxO2jOHsPbt1QAcNiCfncN2cVX2bK4uKoxpT0MO\nj+jDM5HDMHp+1Trjzat+2Nf0J6RTp9C616+Hww4Lreezz2Dr1r2/B9u3Q1kZbNkCXbrATTfBmDFI\nlFSM+JMN/sHARHcvCk+PB3D3X0WVeRB4w92fCk8vAQqBnjXVDZcZ4u5rzSwXKHH3I+NsX8FfZcqU\n0FGyZ0/s/LQ0yMiAFi1Cjyrt24eOvC1bQkdhZSWUl8Mhh0CrVrBzJ+zaBS1bhqb37Akd1VVvINLS\nQnV69IC2bUPbeP/90PLeveGTT+C440Lbeu+90PP27UNvMiBU/t//DrWhf//QtiHUlq+/jl+nvst2\n74ZRo+DPfw71q751f/nL0PK7745fv671V18OsduExNaRSDuqyowfDx99FNrXe/bAMcfAr34Vm7bL\nl+9dV1UbfvnL/RL+iWyqqsyOHbG/Eq1b138XNPQlTvU6GrLcu9/Jo9smwOzwCzMcjllyJyfk3dzg\nQyD6cKs6PL/73b2HW02HYfT8I44IHc59+sCyZfvOW75872H/0Ueh5a1bx/4JMQu9QYDQmGPjxtCv\np1m47x56VFbu/b0wC/3pefBBhX+0pnCqPx9YGTVdFp6XSJm8Wup2dve14edrgc5JtvPgd//9oZ9W\n7fehKtArKvaGv3vorfW2baG/QlUhvmVL6GjMyQn93Lp173RmZugI//TT0POcnFDgf/pp6IjeujU0\nnZkJX3wB6emheVu37n2emxsqW1U+MzNUZ+vWvfNzc2uuU99lhxwCjz4a+tmQum+8EXrUVL+u9Vdf\nXn2bia4jkXZUlVm3LvSaVu2zdev2DgWrRK8ruv5+kMimqspU/5VoyC5o6Euc6nXUd3lGhvP0rx8L\nhf4l4cds+HTeY3Tu7EkfHtGHZ/ThVtNhGD2/6nD+4ov486IP+127Qn9Kqv8JSUvbG+47doR+7tkT\nKmu2b+hDaH55+d4/bZI66UnWT3S4nci7E4u3Pnd3M6txO8XFxZHnhYWFFBYWJtgkEZGmobR0Djt3\nfrnP/F271vDJJy8Aww58o6RJKCkpoaSkJKXrTDb4VwHdoqa7ERq511ama7hMRpz5q8LP15pZrrt/\naWZdgHU1NSA6+APtmmtCp/qrf/TRosXeU/1Vb6nNoE2bvaf69+wJLW/XLvTWfN260M+2bfdO79kT\nOr9Xdap/+/bQ+nr12nuqf+vW2FP9bduGtldREXr+5ZehoQCEyn/zTagNbduGzgdCqEzbtvHr1HfZ\n7t1wySWh86sNqVv1gef8+Q1bf/XlELtNSGwdibSjqswrr4TOt27fHtpnPXrsXVbl5JP3rquqDdXL\npEgim6oq07Zt7K9EQ3YBNOwlTvU66rN8zRrnzTd/QUXXrTAceDT8wgyHPbO38tJLv+C00/4LM2vw\n4VH98Kw63Go6DKPnV53WP/zwfU/1H3547Kn+LVv2ntaP/hNSdVofQh8D7NgRmm8Waq9Z7J8oCK0z\nIyP0py3Iqg9ob7vttqTXmexn/OmELtA7FVgNLKD2i/sGAfeGL+6rsW744r6v3P2e8Gf/Wbq4LwG6\nuE8X9+nivmZ3cd8HH/yFh+ddwK5hO0On+leEX5QewHDIeL4V//Pzpzj11GG6uE8a/+K+cCPOBO4F\n0oCH3X2SmV0F4O4PhcvcBxQB24Cx7v7vmuqG53cAZgEFhA6DEe6+Oc62Ffwi0my5O11P6srqE1bH\nhn6VHsBwyH8zn5X/XIlVv4ZHAqdJBH9jUvCLSHM26YlJ/PL9X8YP/So9gOFwd/+7uWnkTQesbdI0\nKfgV/CLSTJWsKOHcJ85l2K5h9KBHrWVXsII5Lefw7MhndSOfgEtF8Cd7cZ+IiNRT1R356hPkuouf\npIq+pEdE5ABqaIAn+5W+IlUU/CIiB0iyo3aFv6SCgl9E5ABI1al6hb8kSxf3iYjsZ/NXzmfYk8NS\n+vl81RuJORfMYXC3wSlZpzR9uqpfwS8izcCmHZtYsmFJygN6/sr5HHnYkWS3zk7peqXpUvAr+EVE\nJECawrfziYiISDOi4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0REJEAU\n/CIiIgGi4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0REJEAU/CIiIgGi\n4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0REJECSCn4z62Bmr5nZJ2b2\nqpll1VCuyMyWmNkyM7uxrvpmdrqZvWtmi8I/T06mnSIiIhKS7Ih/PPCau/cB5oWnY5hZGnAfUAT0\nBUaa2VF11F8P/MDd+wEXA39Ksp0iIiICmLs3vLLZEmCIu681s1ygxN2PrFZmMDDR3YvC0+MB3P1X\nCdY3YAOQ6+7l1ZZ5Mu0XERFpTswMd7dk1pHsiL+zu68NP18LdI5TJh9YGTVdFp6XaP3zgPeqh76I\niIjUX3pdBczsNSA3zqKboyfc3c0s3vC7+jyLMy9ufTM7GvgVcHpd7RQREZG61Rn87l5j6JrZWjPL\ndfcvzawLsC5OsVVAt6jpruF5ADXWN7OuwLPARe7+eU1tKC4ujjwvLCyksLCwri6JiIg0CyUlJZSU\nlKR0ncl+xj8Z+Mrd7wl/dp/l7uOrlUkHlgKnAquBBcBId19cU/3w1f1/J3RtwPO1bF+f8YuISGCk\n4jP+ZIO/AzALKABWACPcfbOZ5QHT3f2scLkzgXuBNOBhd59UR/1bCF3hvyxqc6e7+4Zq21fwi4hI\nYDR68Dc2Bb+IiARJU7iqX0RERJoRBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0RE\nJEAU/CIiIgGi4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0REJEAU/CIi\nIgGi4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0REJEAU/CIiIgGi4BcR\nEQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0REJEAU/CIiIgGi4BcREQmQBge/\nmXUws9fM7BMze9XMsmooV2RmS8xsmZndmGh9Mysws61m9vOGtlFERERiJTPiHw+85u59gHnh6Rhm\nlgbcBxQBfYGRZnZUgvV/A7yYRPtERESkmmSCfxjwWPj5Y8A5ccoMBJa7+wp3LweeBM6uq76ZnQN8\nBnycRPtERESkmmSCv7O7rw0/Xwt0jlMmH1gZNV0WnldjfTNrC9wAFCfRNhEREYkjvbaFZvYakBtn\n0c3RE+7uZuZxylWfZ3HmVa9fDPzW3bebmdXWPhEREamfWoPf3U+vaZmZrTWzXHf/0sy6AOviFFsF\ndIua7hqeB1BT/YHAeWY2GcgCKs1sh7vfH68dxcXFkeeFhYUUFhbW1iUREZFmo6SkhJKSkpSu09zj\nDdQTqBgK5q/c/R4zGw9kufv4amXSgaXAqcBqYAEw0t0XJ1h/IvCNu/+mhjZ4Q9svIiLS3JgZ7p7U\n2fBkPuP/FXC6mX0CnBKexszyzOxFAHevAMYBrxC6UO8pd19cW30RERHZfxo84m8KNOIXEZEgaewR\nv4iIiDQzCn4REZEAUfCLiIgEiIJfREQkQBT8IiIiAaLgFxERCRAFv4iISIAo+EVERAJEwS8iIhIg\nCn4REZEAUfCLiIgEiIJfREQkQBT8IiIiAaLgFxERCRAFv4iISIAo+EVERAJEwS8iIhIgCn4REZEA\nUfCLiIgEiIJfREQkQBT8IiIiAaLgFxERCRAFv4iISIAo+EVERAJEwS8iIhIgCn4REZEAUfCLiIgE\niIJfREQkQBT8IiIiAaLgFxERCRAFv4iISIAo+EVERAJEwS8iIhIgDQ5+M+tgZq+Z2Sdm9qqZZdVQ\nrsjMlpjZMjO7MZH6ZtbPzOab2UdmtsjMWja0nSIiIrJXMiP+8cBr7t4HmBeejmFmacB9QBHQFxhp\nZkfVVt/M0oE/AVe6+7eBIUB5Eu0UERGRsGSCfxjwWPj5Y8A5ccoMBJa7+wp3LweeBM6uo/4ZwCJ3\n/xDA3Te5e2US7RQREZGwZIK/s7uvDT9fC3SOUyYfWBk1XRaeV1v9PoCb2V/N7D0z+39JtFFERESi\npNe20MxeA3LjLLo5esLd3cw8Trnq8yzOvOr104HvAwOAHcA8M3vP3V+vra0iIiJSt1qD391Pr2mZ\nma01s1x3/9LMugDr4hRbBXSLmu4angdQU/2VwD/cfWN4Oy8B3wXiBn9xcXHkeWFhIYWFhbV1SURE\npNkoKSmhpKQkpes093gD9QQqmk0GvnL3e8xsPJDl7uOrlUkHlgKnAquBBcBId19cU30zywb+RmjU\nXw68DPzG3V+O0wZvaPtFRESaGzPD3S2pdSQR/B2AWUABsAIY4e6bzSwPmO7uZ4XLnQncC6QBD7v7\npNrqh5eNAm4i9LHAi9XfUES1QcEvIiKB0ajB3xQo+EVEJEhSEfy6c5+IiEiAKPhFREQCRMEvIiIS\nIAp+ERGRAFHwi4iIBIiCX0REJEAU/CIiIgGi4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGR\nAFHwi4iIBIiCX0REJEAU/CIiIgGi4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iI\nBIiCX0REJEAU/CIiIgGi4BcREQkQBb+IiEiAKPhFREQCRMEvIiISIAp+ERGRAFHwi4iIBIiCX0RE\nJEAU/CIiIgGi4BcREQkQBb+IiEiANDj4zayDmb1mZp+Y2atmllVDuSIzW2Jmy8zsxrrqm1krM3vC\nzBaZ2cdmNr6hbRQREZFYyYz4xwOvuXsfYF54OoaZpQH3AUVAX2CkmR1VR/0LANy9H3AccJWZFSTR\nzmappKSksZuwX6l/zZv613wdzH2Dg79/qZBM8A8DHgs/fww4J06ZgcByd1/h7uXAk8DZddRfAxwa\nftNwKLAb2JJEO5ulg/2XV/1r3tS/5utg7hsc/P1LhWSCv7O7rw0/Xwt0jlMmH1gZNV0WnldjfXd/\nhVDQrwFWAFPcfXMS7RQREZGw9NoWmtlrQG6cRTdHT7i7m5nHKVd9nsWZF1PfzEYDrYEuQAfgn2Y2\nz90/r62tIiIiUjdzj5fXCVQ0WwIUuvuXZtYFeMPdj6xWZhBQ7O5F4embgEp3v6em+mZ2P/Cmu88M\n13kY+Ku7z47ThoY1XkREpJlyd0umfq0j/jrMAS4G7gn/fD5OmXeB3mbWA1gNnA+MrKP+EuAUYKaZ\nHQoMAn4brwHJdl5ERCRokhnxdwBmAQWEPosf4e6bzSwPmO7uZ4XLnQncC6QBD7v7pDrqtwQeBr5D\n6BqEP7j71Ab3UERERCIaHPwiIiLS/DTpO/clcpMgM+tmZm+Y2X/M7CMzu7Y+9RtTPW6C9AczW2tm\nH1abX2xmZWb2fvhRdGBanpgU9O9g2X813cSqye2/mtparcy08PKFZta/PnUbW5L9WxG+sdj7Zrbg\nwLU6cXX1z8yONLP5ZrbTzH5en7pNQZL9a9L7L4G+jQr/Ti4ys/8zs36J1t2HuzfZBzAZuCH8/Ebg\nV3HK5ALHhp+3BZYCRyZav6n3L7zsJKA/8GG1+ROB6xu7H/uxf81+/xH6iGs50APIAD4AjmqK+6+2\ntkaVGQq8FH5+PPBWonUb+5FM/8LTnwMdGrsfSfavEzAAuBP4eX3qNvYjmf419f2XYN8GA+3Dz4uS\nOfaa9IifBG4S5O5fuvsH4edbgcXsvVdAIjcZakwJtc/d/wlsqmEdTfkCx2T7dzDsv9puYgVNa//V\n1VaI6rO7vw1kmVlugnUbW0P7F32Pkqa0v6qrs3/uvt7d3wXK61u3CUimf1Wa6v5LpG/z3f3r8OTb\nQNdE61bX1IM/kZsERYT/e6A/oRel3vUbQSra95Pw6Z+Hm9qpcJLv38Gw/2q7iRU0rf1XV1trK5OX\nQN3Glkz/IHQPkr+Z2btmdsV+a2XDJdK//VH3QEm2jU15/9W3b5cBLzWwblL/zpcSlvxNgqrW0xZ4\nGrguPPKPUVf9/SVV/avBA8Dt4ed3AFMJ/UIcMPu5fymr31Ap6F9tbW70/VdNoq9vUx011SXZ/n3f\n3VebWSfgNTNbEj5b1VQkc3w0h6u8k23jie6+ponuv4T7ZmYnA5cCJ9a3bpVGD353P72mZeELvnJ9\n701+1tVQLgN4Bpjp7tH3E0io/v6Uiv7Vsu5IeTObAbzQ8JY2zP7sHwfH/lsFdIua7kboHXmT2H/V\n1NjWWsp0DZfJSKBuY2to/1YBuPvq8M/1ZvYcoVOsTSU4ILH+7Y+6B0pSbXT3NeGfTXH/JdS38AV9\n04Eid99Un7rRmvqp/qqb/EANNwkyMyP0f/8fu/u99a3fyJJqXzhsqvwQ+LCmso0k2df/YNh/kZtY\nmdkhhG5iNQea5P6rsa1R5gBjIHJnzs3hjzsSqdvYGtw/M2tjZpnh+YcCZ9D4+6u6+uyD6mc1Dpb9\nVyWmf81g/9XZNwt9S+2zwGh3X16fuvto7KsZ67jSsQPwN+AT4FUgKzw/D3gx/Pz7QCWhKxnfDz+K\naqvfVB6J9C88/QShOx/uIvRZztjw/D8Ci4CFhEKnc2P3KcX9O1j235mE/ttkOXBT1Pwmt//itRW4\nCrgqqsx94eULge/W1c+m9Gho/4DDw39jPgA+aq79I/Sx1Urga0IX1H4BtD1Y9l9N/WsO+y+Bvs0A\nvmJvzi2orW5tD93AR0REJECa+ql+ERERSSEFv4iISIAo+EVERAJEwS8iIhIgCn4REZEAUfCLiIgE\niIJfREQkQBT8IiIiAfL/AQh9VI9k9a8RAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106d9cc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(alphas[y==0, 0], np.zeros((50)), color='red', alpha=0.5)\n",
    "plt.scatter(alphas[y==1, 0], np.zeros((50)), color='blue', alpha=0.5)\n",
    "plt.scatter(X_proj, 0, color='black', label='original projection of point X[24]', marker='^', s=100)\n",
    "plt.scatter(x_reproj, 0, color='green', label='remapped point X[24]', marker='x', s=500)\n",
    "plt.legend(scatterpoints=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[[back to top](#Sections)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] Q. Wang. [Kernel principal component analysis and its applications in face recognition and active shape models](http://arxiv.org/abs/1207.3538). CoRR, abs/1207.3538, 2012.\n",
    "\n",
    "[2] B. Scholkopf, A. Smola, and K.-R. Muller. [Kernel principal component analysis](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.128.7613). pages 583–588, 1997.\n",
    "\n",
    "[3] B. Scholkopf, A. Smola, and K.-R. Muller. [Nonlinear component analysis as a kernel eigenvalue problem](http://www.mitpressjournals.org/doi/abs/10.1162/089976698300017467#.VBh9QkuCFHg). Neural computation, 10(5):1299–1319, 1998.\n",
    "\n",
    "[4] S. T. Roweis and L. K. Saul. [Nonlinear dimensionality reduction by locally linear embedding](http://www.sciencemag.org/content/290/5500/2323.short). Science, 290(5500):2323–2326, 2000.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
